Automatic Response Category Combination in Multinomial Logistic Regression

Bradley S. Price; Charles J. Geyer; Adam J. Rothman

doi:10.1080/10618600.2019.1585258

Automatic Response Category Combination in Multinomial Logistic Regression

Bradley S. Price, Charles J. Geyer, Adam J. Rothman

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is nondifferentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm’s convergence. Prediction and model selection are also addressed. Supplemental materials for this article are available online.

Original language	English (US)
Pages (from-to)	758-766
Number of pages	9
Journal	Journal of Computational and Graphical Statistics
Volume	28
Issue number	3
DOIs	https://doi.org/10.1080/10618600.2019.1585258
State	Published - Jul 3 2019

Bibliographical note

Funding Information:
This research is partially supported by the National Science Foundation grant DMS-1452068. The authors thank the referees and the associate editor for helpful comments.

Publisher Copyright:
© 2019, © 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Keywords

Fusion penalty
Multinomial logistic regression
Response category reduction

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10.1080/10618600.2019.1585258

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abstract = "We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is nondifferentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm{\textquoteright}s convergence. Prediction and model selection are also addressed. Supplemental materials for this article are available online.",

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AU - Geyer, Charles J.

AU - Rothman, Adam J.

N1 - Funding Information: This research is partially supported by the National Science Foundation grant DMS-1452068. The authors thank the referees and the associate editor for helpful comments. Publisher Copyright: © 2019, © 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

PY - 2019/7/3

Y1 - 2019/7/3

N2 - We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is nondifferentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm’s convergence. Prediction and model selection are also addressed. Supplemental materials for this article are available online.

AB - We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is nondifferentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm’s convergence. Prediction and model selection are also addressed. Supplemental materials for this article are available online.

KW - Fusion penalty

KW - Multinomial logistic regression

KW - Response category reduction

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Automatic Response Category Combination in Multinomial Logistic Regression

Abstract

Bibliographical note

Keywords

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